🤖 AI Summary
Existing dimensionality reduction methods often trade off representational capacity against interpretability. This paper proposes the Weighted Linear Transformation (WLT) framework, which jointly models nonlinear manifold structures via multiple learnable linear mappings weighted by a Gaussian kernel—thereby embedding strong nonlinear expressivity into an analytically tractable linear architecture for the first time. WLT enables per-mapping interpretation, quantification of dimensional importance, and visualization of spatial deformations, and introduces geometrically sensitive explanatory tools such as Jacobian field analysis. On multiple benchmark datasets, WLT achieves visualization quality comparable to t-SNE and UMAP, while providing reproducible, verifiable quantitative interpretability metrics. An open-source toolkit supports interactive diagnostic analysis and practical deployment.
📝 Abstract
Dimensionality reduction techniques are fundamental for analyzing and visualizing highdimensional data. With established methods like t-SNE and PCA presenting a trade-off between representational power and interpretability. This paper introduces a novel approach that bridges this gap by combining the interpretability of linear methods with the expressiveness of non-linear transformations. The proposed algorithm constructs a non-linear mapping between high-dimensional and low-dimensional spaces through a combination of linear transformations, each weighted by Gaussian functions. This architecture enables complex non-linear transformations while preserving the interpretability advantages of linear methods, as each transformation can be analyzed independently. The resulting model provides both powerful dimensionality reduction and transparent insights into the transformed space. Techniques for interpreting the learned transformations are presented, including methods for identifying suppressed dimensions and how space is expanded and contracted. These tools enable practitioners to understand how the algorithm preserves and modifies geometric relationships during dimensionality reduction. To ensure the practical utility of this algorithm, the creation of user-friendly software packages is emphasized, facilitating its adoption in both academia and industry.